Question

A train covered a certain distance at a uniform speed. if the train would have been 10 km/h faster, it would have taken 2 hours less than the scheduled time. and if the train were slower by 10 km/h; it would have taken 3 hours more than the scheduled time. find the distance covered by the train.

Answer 1

Solution:-
Let the speed of the train be 's', time taken by the train be 't' and the distance covered by it be 'd'.
Speed = distance/ time
s = d/t
⇒ d = st   .........(1)
Case No. 1
If the train would been 10 km/h faster,
(s+10) = d/(t-2)
⇒ (s+10) (t-2) = d
⇒ st + 10t - 2s - 20 = d
Putting the value of d = st in above, we get
⇒ st = st + 10t -2s -20
⇒ 10t - 2s = 20  .......(2)
Case No. 2
If the train would have been slower by 10 km/h,
(s-10) = d/(t+3)
⇒ (s-10) (t+3) = d
⇒ st - 10t + 3s - 30 = d
Putting the value of d = st in above, we get
st = st - 10t + 3s - 30
⇒ - 10t + 3s = 30 .......(3)
Adding the equations (1) and (2), we get
  10t - 2s = 20
- 10t +3s = 30
____________
           s = 50 
____________
Putting the value of s= 50 in the equation (2), we get
⇒ 10t - 2 × 50 = 20
⇒ 10t - 100 = 20
⇒ 10t = 120
⇒ t = 120/10
⇒ t = 12 hours.
Putting the value of t = 12 in the equation (1), we get
⇒ d = 50 × 12
⇒ d = 600 km
The distance covered by the train is 600 km.